运用唯物辩证法于数学基础的一个范例——重新解读马克思的《论导函数概念》等文

An Example of Dialectical Materalist Methods to Mathematical Foundation——A Fresh Understanding of《On Derivative Concept》by Carl Marx

依据唯物辨证法 ,指出目前的极限概念应用于求导数的运算时在概念及数值两方面都有矛盾 ,强调诚如马克思所言 ,在求导数的运算时的Δx→ 0的正确含义最终应该是Δx=0 ,导数的真值应该是dy/dx =(0 /0 ) =… ,它是特定的 (0 /0 ) ,是隐含于原函数中的可导点处的新关系的准确值 .

Based itself on dialectical materialism, this paper points out that when the “limit concept” was applied to proving the derivative, it will result in some contradictions both in concept and in value, then the paper emphasizes that the correct implication of Δx→0 should befinally Δx=0 when the derivative is to be proved. The actual value of the derivative should be dy/dx=(0/0)=…. But the value is the specific (0/0). It is a correct value of the fresh relation hidden at the point where there is the derivative of the original function, just as Carl Marx said. The paper also points out at last that correctness of this conclusion is true.